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## Homework Statement

.[/B]I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency.

## Homework Equations

.[/B]\begin{align*}

\frac{2\omega n L}{c} &= 2m\pi

\end{align*}

\begin{align*}

n_g &= n + \omega \frac{dn}{d\omega}

\end{align*}

**3. The attempt at the solution.**

I have considered a uniform plane wave propagating within the cavity satisfying the following relation

\begin{align*}

\frac{2\omega n L}{c} &= 2m\pi

\end{align*}

where ω is the angular frequency, n is the effective refractive index and L is the length of the laser cavity. I have derived the group refractive index as follows

\begin{align*}

n_g &= n + \omega \frac{dn}{d\omega} \\

&= \frac{c m \pi}{\omega L} - \frac{c m \pi}{ \omega L}\\

&= 0

\end{align*}

If this is correct, I don't understand what this is physically entailing. Any insight would be much appreciated! Thank you.